Trustworthy Digital Representations of Analog Information—An Application-Guided Analysis of a Fundamental Theoretical Problem in Digital Twinning †
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
This article compares two methods of algorithmically processing bandlimited time-continuous signals in light of the general problem of finding “suitable” representations of analog information on digital hardware. Albeit abstract, we argue that this problem is fundamental in digital twinning, a signal-processing paradigm the upcoming 6G communication-technology standard relies on heavily. Using computable analysis, we formalize a general framework of machine-readable descriptions for representing analytic objects on Turing machines. Subsequently, we apply this framework to sampling and interpolation theory, providing a thoroughly formalized method for digitally processing the information carried by bandlimited analog signals. We investigate discrete-time descriptions, which form the implicit quasi-standard in digital signal processing, and establish continuous-time descriptions that take the signal’s continuous-time behavior into account. Motivated by an exemplary application of digital twinning, we analyze a textbook model of digital communication systems accordingly. We show that technologically fundamental properties, such as a signal’s (Banach-space) norm, can be computed from continuous-time, but not from discrete-time descriptions of the signal. Given the high trustworthiness requirements within 6G, e.g., employed software must satisfy assessment criteria in a provable manner, we conclude that the problem of “trustworthy” digital representations of analog information is indeed essential to near-future information technology.
Details
Originalsprache | Englisch |
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Aufsatznummer | 514 |
Fachzeitschrift | Algorithms |
Jahrgang | 16 |
Ausgabenummer | 11 |
Publikationsstatus | Veröffentlicht - Nov. 2023 |
Peer-Review-Status | Ja |
Externe IDs
ORCID | /0000-0001-8469-9573/work/161891067 |
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Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- bandlimited signals, computability, computable analysis, digital twinning, interpolation, sampling, Shannon series, trustworthiness, Turing machines